The three-time All-Star threw twice recently at the University of San Francisco in front of Giants pitching coach Dave Righetti and bullpen catcher Bill Hayes. The team thinks Wilson, 31, is close to being major league ready.

From 2008 to 2011, Wilson was among the most effective closers in the majors, saving 163 games in that span. He helped lead San Francisco to the 2010 World Series title with 48 regular season and six postseason saves

But during the 2012 season, Wilson appeared in only two games before having Tommy John surgery. It was the second time he has had the ligament-replacement procedure on his pitching elbow. The team nontendered him after the season, and he was unable to land a free agent deal.

“We try to stay in touch with his process and monitor his progress,” Evans said. “Ultimately, his rehab is our responsibility. Again he’s a Giant, and we’ve been in touch with his people throughout the winter as he considers his options.”

With lefty reliever Jeremy Affeldt sidelined up to six weeks with a strained left groin, the Giants are looking for bullpen help.